Method and device for measuring at least a geometric quantity of an optically reflecting surface

ABSTRACT

This invention concerns a process and a device for measuring at least one geometric magnitude of an optically reflective surface. The process is rapid, reliable, and precise, and makes it possible to quantify the curvatures and/or slopes and reliefs of the optically reflective surface without the risks of damaging the surface to be measured, and which is suitable for measuring large surfaces.  
     The process for geometric measurement of an optically reflective surface to be measured S consists of using a camera ( 2 ) to observe the image of this surface to be measured S placed in a measuring space ( 1 ), then interpreting the image of this surface to be measured S viewed by the camera ( 2 ) as a function of images obtained previously by calibration of a reference surface to transform this image into quantitative values characterizing at least one geometric magnitude of the optically reflective surface to be measured S.

TECHNICAL BACKGROUND

[0001] This invention pertains to a process and a device for measuringat least one geometric magnitude of an optically reflective surface.

PRIOR ART

[0002] There are a number of procedures and devices by which one canobserve the geometry of surfaces in general.

[0003] One of these procedures, particularly suitable for applicationsin the automotive and aeronautic industries, consists of using anoptical device with a camera directed toward the surface to be observed,this camera being connected to a computer and generating an image inshades of gray, showing variations in the surface's curvature. Devicesof this kind are marketed, for example, under the trademarks DIFFRACTO®and ONDULO®, and are generally used for optically reflective surfaces,permitting qualitative readings by means of images in shades of gray. Inthis way, these devices can be used to visualize slight variations inslope or curvature by using the principle of specular reflection, butthey do not permit quantitative readings of geometrical magnitudes ofthese variations. Therefore, it is impossible to know the value of theslopes or curvatures of the optically reflective surfaces.

[0004] Other known procedures make it possible to measure geometricmagnitudes of these optically reflective surfaces.

[0005] A first procedure consists of using a mechanical feeler thatmoves in relation to the optically reflective surface to be measured.This mechanical feeler is calibrated so that one or more geometricmagnitudes of the surface can be made to correspond to each displacementof its measuring finger. At the time of measurement, the finger of themechanical feeler generally follows a predetermined path to sweep theentire surface. In this way, it is possible to measure the geometricmagnitude(s) of the path followed according to the axis of themechanical feeler. The greatest disadvantages of this procedure are thetime needed to measure the surface, the lack of precision resulting fromthe limited number of measuring points, and finally the risks of surfacedamage from contact with the finger of the mechanical feeler.

[0006] A second known procedure uses the techniques of interferometry.This procedure compares two waves from the same laser, one reflected bythe surface to be measured, and the other a reference coming directlyfrom the laser. Like the previous procedure, the latter is suitable formeasuring small surfaces. However, for measuring large surfaces such asmirrors, windshields, and others, this process is particularly expensiveand time-consuming. In addition, this process is appropriate only forperfect optically reflective surfaces, which does not describe thepanels of automobile bodies, for example.

[0007] Therefore, existing procedures do not permit a rapid and precisemeasurement of large optically reflective surfaces.

DESCRIPTION OF THE INVENTION

[0008] This invention aims to remedy these disadvantages by offering aprocedure and a measuring device to measure at least one geometricmagnitude of an optically reflective surface; this device is rapid,reliable, and precise, and with it one can quantify the curves and/orslopes and reliefs of the optically reflective surface without risk ofdamaging the surface to be measured; in addition, it is suitable formeasuring large-sized optically reflective surfaces.

[0009] To this end, the invention concerns a procedure as defined above,in which a camera is used to view the image of the optically reflectivesurface to be measured S, characterized in that this procedure involvesat least one calibration phase and at least one measurement phase, andin that the calibration phase is accomplished to permit interpretationof the image of the surface to be measured S viewed by the camera duringthe measuring phase, and thereby to transform this image intoquantitative values characterizing at least one geometric magnitude ofthe optically reflective surface to be measured S.

[0010] To carry out the phases of calibration and measurement, it isadvantageous to define a measurement space associated with anorthonormed reference mark O, X, Y, Z. In this measuring space, there isat least one optically reflective reference surface P, Ci, or surface tobe measured S. The camera is disposed so that its field of view coversthe measuring space, and an image can be visualized in association witha plane reference mark O′, X′, Y′. There is also a test image associatedwith a plane reference mark O″, X″, Y″ and having reference points M″iso that its reference points M″i reflecting on said reference surface P,Ci or surface to be measured S or in points Mi, with the camera one canobserve the viewed points M′i image of the reference points M″i afterreflection on the reference surface P, Ci or surface to be measured S atpoints Mi, and a single correspondence is established between the viewedpoints M′i and the reference points M″i.

[0011] Preferably, the calibration phase includes a flat calibrationstep, in which a single correspondence is established between thecoordinates x′, y′ of the viewed points M′i and the coordinates x, y ofthe points Mi, of which the coordinate according to the axis Z is known.

[0012] In a first embodiment, the calibration phase includes a curvedcalibration step for which a camera is available, so that its field ofview is oblique to the reference surface Ci, the test image is situatedopposite the camera in relation to the reference surface Ci, and thecamera is focused essentially at the level of the reference surface Ci.

[0013] It is particularly advantageous to use as a reference surface atleast one standard curve Ci having at least one known curve/Ri along oneof the axes X, Y, to observe with the camera the viewed points M′i imageof the reference points M″i of the test image after reflection on thestandard curve Ci at points Mi, and to establish a single correspondencebetween the values measured at viewed points M′i or their variations andthe curve 1/Ri of the standard curve Ci. In one embodiment variation,the test image includes an intensity code Ii and/or color code thatvaries from one point to another of the test image surface, thisvariation being defined by a known function along at least one axisX″,Y″ of the test image, and with the camera we can observe the viewedpoints M′i image of the reference points M″i of the test image afterreflection on the standard curve Ci at points Mi, and we establish asingle correspondence between the intensity I′i measured and or thecolor measured or their variation at the viewed points M′i and the curve1/Ri of the standard curve Ci.

[0014] It is preferable to shift the standard curve Ci forming thereference surface in different positions of the measuring space, and werepeat the observation of the image viewed by the camera and theestablishment of the single correspondence in a number of points Midetermined as a function of the desired precision for said singlecorrespondence. We can then use several standard curves Ci each having adifferent 1/Ri curve.

[0015] In a first mode of embodiment, to accomplish the curve measuringphase, the optically reflective surface to be measured S isadvantageously placed in the space to be measured, and with the camerawe observed the viewed points M′i image of the reference points M″i ofthe test image after reflection on the surface to be measured S atpoints Mi, and from it we deduce the curve 1/Ri at points Mi as afunction of the laws of single correspondence from the calibrationphase.

[0016] In a second mode of embodiment, the calibration phase includes astep of calibration in slope for which we have the test imageessentially opposite the measuring space and the camera such that itsoptical center is essentially disposed in the vicinity of the testimage, and as a reference surface we use at least one reference plane Pthat is essentially parallel to the test image, and with a knowncoordinate along axis Z.

[0017] To accomplish the calibration phase in slope, it is preferable touse as a reference plane P an essentially flat mirror with coordinateszi along the axis Z; with the camera we observe the viewed points M′iimage of the reference points M″i after reflection on the referencesurface P at points Mi, and we establish the single correspondencebetween the coordinates x′, y′ of the viewed points M′i and thecoordinates x, y of the points Mi of which the coordinate along axis Zis known.

[0018] It is advantageous to shift the mirror forming the referenceplane P parallel to itself in different coordinates zi of the measuringspace, and we repeat the observation of the image viewed with the cameraand establishment of the single correspondence.

[0019] In an embodiment variant, the test image includes a coding ofintensities Iix, Iiy and/or of colors varying from one point to anotherof its surface, these variations being defined by known functions alongaxes X″ and Y″, respectively, of the test image. With the camera, weobserve the viewed points M′i image of the reference points M″i afterreflection on the mirror at points Mi, and we establish singlecorrespondences between the measured intensities I′ix, I′iy on the onehand, and/or the colors measured or their variations at the viewedpoints M′i, and the coordinate zi of the reference plane P, and on theother hand the coordinates xi, yi of point Mi.

[0020] In the second mode of embodiment, to accomplish the slopedmeasuring phase, we place the optically reflective surface to bemeasured S in the measuring space, and with the camera we observe theviewed points M′i image of the reference points M″i of the test imageafter reflection on the surface to be measured S at points Mi. Fromthis, we deduce the coordinates xi, yi, zi at points Mi as a function ofthe laws of single correspondence from the calibration phase, and fromit we deduce the slopes Pix, Piy of the axes X and Y, respectivelybetween two nearby points Mi.

[0021] The invention also concerns a device to implement the procedurefor measuring at least one geometric magnitude of an opticallyreflective surface to be measured S as defined above, characterized inthat it comprises at least one measuring space in which we place atleast one reference surface P, Ci, or surface to be measured S, at leastone reference surface P, Ci designed to calibrate said device, at leastone test image positioned to reflect on said reference surface P, Ci orsurface to be measured S, at least one camera positioned so that itsfield of view covers the measuring space and sees the image of the testimage on said reference surface P, Ci or surface to be measured S, thecamera being associated with a computer system that can interpret theimage of the surface to be measured S seen by the camera and to deducefrom it the quantitative values characterizing at least one geometricmagnitude of the surface to be measured S as a function of at least onereference surface P, Ci.

BRIEF DESCRIPTION OF FIGURES

[0022] This invention and its advantages will become more apparent fromthe following description of embodiment examples, with reference to theattached figures in which:

[0023]FIG. 1 schematically represents the measuring device according tothe invention in an orthonormed spatial reference mark O, X, Y, Z,

[0024]FIG. 2 schematically represents the configuration of the measuringdevice to accomplish the curved calibration phase,

[0025]FIG. 3 represents an embodiment variant of a test image used toaccomplish the curved calibration phase or the curved measuring phase,

[0026]FIG. 4 schematically represents the configuration of the measuringdevice to accomplish the sloped calibration phase, and

[0027]FIG. 5 schematically represents the configuration of the measuringdevice to accomplish the sloped measuring phase.

BEST EMBODIMENT OF THE INVENTION

[0028] With reference to the figures, the invention concerns a processand a device whereby metric data can be used to quantify at least onegeometric magnitude of an optically reflective surface to be measured S.

[0029] During this process, a camera 2 is used to view the image of anoptically reflective surface to be measured S disposed in a measuringspace 1.

[0030] The measuring space 1 illustrated by FIG. 1 is previouslydefined. It is associated with an orthonormed spatial reference mark O,X, Y, Z originating from O of axes X, Y, Z. In this measuring space 1,there is an optically reflective or reference surface P, Ci, or ameasuring surface S, and a camera 2 such that its field of view 3 coversthe space to be measured 1. This camera 2 can be used to visualize animage that is associated with a plane reference mark O′, X′, Y′.

[0031] This process includes at least one calibration phase and onemeasuring phase. During the measuring phase, the calibration phase makesit possible to interpret the image of the surface to be measured Sviewed by the camera 2 and to transform this image into quantitativevalues characterizing one or more geometric magnitudes of the surface tobe measured S.

[0032] To accomplish the calibration phase, we use a test image 6, 10associated with a plane reference mark O″, X″, Y″ and having referencepoints M″i such that these reference points M″i are reflected on thereference surface P, Ci at points Mi, and we observe the viewed pointsM′i image of the points Mi. We then establish a single correspondencebetween the viewed points M′i and the reference points M″i, the natureof these single correspondences depending on the method used.

[0033] In fact, it is possible to accomplish this calibration phase bytwo different methods, for one permitting a measure of the curves andfor the other, a measure of the slopes. These two calibration methodsand the corresponding measuring phases are detailed below.

[0034] In a first method of calibration in curvature that isparticularly well suited to record locally the curves 1/Ri andparticularly to detect any defect of curvature, the camera 2 is orientedas illustrated in FIG. 2 so that its field of view 3 is oblique withrespect to the reference surface P, Ci. We have a test image 6 such thatit is situated opposite the camera 2 with respect to the referencesurface P, Ci and so that the camera 2 sees the image of the test imageon this reference surface P. Ci.

[0035] The method of calibration in curvature may comprise an optionalstep of calibration of the plane. This step, illustrated by FIG. 1,consists of calibration of a reference plane P having coordinate pointsxi, yi in the spatial reference mark O, X, Y, Z of which the coordinatezi along axis Z is known. This optional step will make it possible, ifnecessary, to know, in addition to the curvature 1/Ri at a point Mi, itscoordinates xi, yi as well. Depending on the field of application, theknowledge of these coordinates xi, yi may or may not be necessary.

[0036] In order to carry out this optional step of calibration of theplan, we place essentially in the reference plane P a test image 5 madeup of any surface that can provide a single correspondence between oneof its points Mi and the viewed point M′i corresponding to its image.This single correspondence is established, for example, by means of apattern at known dimensional parameters. This pattern may be made up,for example, of one or more networks of lines forming a grid, forexample. This pattern may also be made up as illustrated in FIG. 1 by anetwork of points or any other pattern made visible on the surface ofthe test image 5 by a known marking or engraving process such asprinting, chemical etching, etc. It is also possible to use a test image5 having a pattern of which the dimensional parameters are not known atthe start, and for which a previous operation is carried out todetermine these dimensional parameters for any known measuring process.

[0037] With the camera 2 we visualize the viewed points M′i, images ofthe points Mi of the test image 5 essentially merged with the referenceplane P. We process this image in such a way as to define thecoordinates x′i, y′i of each viewed point M′i in the plane referencemark O′, X′ Y′ of the image. Each viewed point M′i corresponds, forexample, to a given pixel of the camera 2. In this way, we establish aconversion rule between the coordinates x′i, y′i of the viewed pointsM′i and the coordinates xi, yi of the points Mi. At the end of this flatcalibration step, we can then establish a single correspondence betweeneach pixel or viewed point M′i of the camera 2 and its correspondingpoint Mi, and vice versa. By observing a viewed point M′i, image of apoint Mi belonging essentially to the reference plane P, we are able todetermine the coordinates xi, yi of the point Mi.

[0038] A second curvature calibration step illustrated by FIG. 2consists of calibrating the image viewed by the camera 2 as a functionof a reference surface Ci. We use a reference surface Ci made up, forexample, of at least one standard curve Ci of which the curvature 1/Riis known, Ri being the radius of curvature. In general, we use a seriesof standard curves Ci formed, for example, of massive metal pieces, eachhaving a face corresponding to a cylinder segment or a parabola withknown curvatures 1/Ri. These standard curves Ci are obtained, forexample, by a process of electroerosion, and their faces can be polishedto make them reflective. The standard curves Ci used are chosen to havecurvatures 1/Ri encompassing the various curvatures expected on thesurface to be measured S.

[0039] The reference points M″i of the test image 6 can be brought aboutby markings, for example, circles whose centers have known coordinatesx″i, y″i in the plane reference mark O″, X″, Y″. The test image 6 canalso include a coding of intensity Ii and/or of color, variable from onepoint to another on its surface. The variation of intensity Ii and/or ofcolor on the surface of the test image 6 can also be defined by apredetermined function along at least axis Y″ of the test image 6, andmay correspond, for example, to a sinusoidal function fi. The test image6 is arbitrarily represented in FIG. 2 by a grid.

[0040] A standard curve Ci is placed in the measuring space 1, and thecamera 2 is focused on this standard curve Ci. With the camera 2 weobserve the viewed points M′i, images of the reference points M″i of thetest image 6 after reflection on the standard curve Ci at points Mi, andwe establish a single correspondence between the variations in thevalues measured at viewed points M′i and the known curvature 1/Ri of thestandard curve Ci. The standard curve Ci is shifted into differentpositions of the measuring space 1, the observation of the image viewedby camera 2 is repeated, and the single correspondence is established.Several standard curves Ci are used, each having a different curvature1/Ri, and the observation of the image viewed by the camera 2 and theestablishment of the single correspondence is repeated. This step,performed at several points Mi of the reference plane with severaldifferent standard curves 1/Ri, makes it possible to deduce a generallaw that is valid for every point Mi and for every curve 1/Ri in thedesired range of curvature. The number of measuring points Mi will bedetermined as a function of the desired precision for the singlecorrespondence.

[0041] In a particular mode of embodiment of the curve calibration, thestandard curve Ci is placed in such a way that its generatrix Gi mergedwith the reference plane P is essentially parallel to the axis Y, andthe camera 2 is focused essentially on the standard curve Ci.Accordingly, the deduced curve 1/Ri will correspond essentially to thecurve 1/Rix along axis X. According to a particular embodiment variantof the curve calibration, the test image 6 comprises an intensity codingIi varying from one point to another of its surface. This variationfollows, for example, a sinusoidal function fi represented on FIG. 2connecting, in a known manner, the light intensity Ii of each referencepoint M″i to its phase φi. Using a method such as temporal phase shift,spatial phase shift, or direct phase calculation by the Fourriertransform of the image formed by the values measured at the viewedpoints M′i, we establish a single correspondence between the intensityI′i observed at viewed points M′i, image of the reference points M′i,with the phase φi. In a second step, this operation is carried out,simultaneously or otherwise, for all or part of the viewed points M″i ofthe image. In general, this operation is performed on as many viewedpoints M′i corresponding to measuring points as there are pixelsinvolved with the standard curve Ci.

[0042] Between the adjacent viewed points M′i, or nearby pixels, wedetermine the derivatives of the phase φi essentially along the axis X.A simple method for completing this derivative essentially along axis Xconsists of diverting along the axis Y′ the plane reference mark O′, X′,Y′ linked to the image viewed by the camera 2. This derivative isgenerally constant over the entire surface of the standard curve Ci.Finally, this phase variation Δφi obtained is associated with the curve1/Rix along the axis X of the standard curve Ci at point Mi. We thenplace the standard curve Ci at different points of the measuring space 1so that the variation in Δφi in measuring space 1 can be measured atdifferent points.

[0043] We then use a second standard curve Ci+1 (not shown) withcurvature 1/Ri+1, also known, with which we repeat these same steps,then possibly with other standard curves having different curvatures,until we are able to establish a general law of the transformation ofthe phase variation Δφi in curvature 1/Rix, the phase variation Δφibeing the variation between the phases φi observed by means of thecamera 2. This phase variation Δφi is calculated between nearby pixelsrepresenting nearby points Mi that are offset with respect to each otheressentially along the axis X, 1/Rix being the corresponding curvature ofthe standard curve Ci or of the surface to be measured S at point Mialong axis X. This general law of transformation can be expressed bymeans of a mathematical equation.

[0044] At the end of this step, the general law of transformation of thephase variation Δφi in curvature 1/Rix makes it possible, by measuringthe phases φi then calculating the phase variations Δφi along axis X atany point Mi of the surface to be measured S situated essentially in theplane P, to know the curvature 1/Rix along the axis X in each of thesepoints Mi. This law will be recorded and the assembly parameters will beset to complete the measuring phase.

[0045] In another embodiment variation, the test image 6 can be obtainedas illustrated by FIG. 3, by projection of at least one projectiondevice 8 of a test image 9 on an intermediate plane 7. The referencepoints M*i of the test image 9 are thereby projected to points M″i ofthe test image 6 and, after reflection at points Mi of the surface to bemeasured S, they are observed in the image of camera 2 at viewed pointsM′i or pixels.

[0046] The curvature calibration phase is followed by the phase ofmeasuring in curvature of the optically reflective surface to bemeasured S. The surface to be measured S is placed in the space to bemeasured 1, with the camera 2 we observe the viewed points M′i image ofthe reference points M″i of the test image 6 after reflection on thesurface to be measured S at points Mi, and from this we deduce thecurvature 1/Ri at points Mi of the surface to be measured S as afunction of the law or laws of single correspondence resulting from theprevious curvature calibration phase or phases.

[0047] In a second method of calibration called sloped calibration,which is particularly suited for measuring the geometric magnitudes of alarge optically reflective surface to be measured S situated in themeasuring space 1, as illustrated by FIG. 4, there is an essentiallyplane test image 10 and a plane reference mark O″, X″, Y″, essentiallyopposite the measuring space 1 and the camera 2, so that its opticalcenter is disposed essentially in the vicinity of the test image 10. Thetest image 10 may also comprise patterns calibrated at the beginning, orrequire a calibrating operation as in the preceding example. This testimage 10 may comprise, like test image 6, a coding of differentintensities of the same color or a coding of different colors. As areference surface, we use at least one reference plane P essentiallyparallel to the test image 10 and known coordinate plane along the axisZ. This reference plane P is, for example, an essentially flat mirror 12with known coordinate zi along axis Z.

[0048] As in the case of the curvature calibration, the first step ofthe slope calibration illustrated by FIG. 4 consists of performing acalibration of the plane to establish a single correspondence betweenthe coordinates of the points Mi in the spatial reference mark O, X, Y,Z, and of which the coordinate along axis Z is known, and thecoordinates of the viewed points M′i in the plane reference mark O′, X′,Y′. In the case of the sloped calibration, this step is indispensable.

[0049] To establish this single correspondence, as for the curvecalibration, the camera 2 is used to observe the viewed points M′i,images of the reference points M″i of the test image 10 after reflectionon the mirror 12 at points Mi. Knowing the coordinates of the referencepoints M″i and of the point M″c, M″c being the optical center of thelens of camera 2, and of coordinates x″c, y″c, it is determined byapplying the laws of the reflection of coordinates of point Mi. In fact,it is known that the coordinates xi, yi along axes X, Y of Mi are equalto half the sums of the coordinates x″c, x″i along axis X and y″c, y″ialong axis Y. In this way, we determine the coordinates xi, yi of Mi forwhich zi is already known. The coordinates x″c, y″c are measured ordetermined empirically, by writing, for example, that the points Mc,M′c, and M″c are aligned, with M′c being the image of Mc afterreflection on the mirror 12 in Mc, and/or that the measurement at M′c isindependent of zc.

[0050] A second step of slope calibration also illustrated by FIG. 4consists of calibrating the axis Z. To accomplish this second step, weshift the mirror 12 forming the reference plane P parallel to itself indifferent known coordinates zi of the measuring space 1, and we repeatthe observation of the image viewed with the camera 2 and establishmentof the single correspondence for the different coordinates zi along theaxis Z. In this way we measure, for each position of the mirror 12, thecoordinates x′i and y′i of the viewed point M′i, image of the referencepoint M″i after reflection on the mirror 12, from which we deduce thecoordinates xi, yi of point Mi of the mirror 12 of the coordinate zialong axis Z. In this way, we obtain the single correspondence betweenthe coordinates x′i, y′i of the viewed point M′i and the coordinates xi,yi of point Mi for each coordinate zi, this single correspondence beingvalid for any point Mi observed by the camera 2 at the viewed point M′ior pixel. This single correspondence is theoretically linear, and forthis reason requires only two measurements to be established. However,because of aberrations, this single correspondence is most oftennonlinear, and requires more measuring points in proportion as it isexpected to be faithful to reality.

[0051] In a particular embodiment variant, the test image 10 comprises acoding of light intensities Iix and Iiy, respectively, along the axesX″, Y″, these intensities varying from one point to another on thesurface. For example, these variations are brought about by means of twosinusoidal functions fix and fiy. In a known manner, the function fixconnects the light intensity Iix along the axis X″ and x″i, for exampleby means of the phase Qix if Iix is modulated sinusoidally along the zisX″. The function fiy in a known manner connects the light intensity Iiyalong the axis Y″ and y″i, for example by means of the phase φiy if Iiyis modulated sinusoidally along axis Y. These sinusoidal functions fix,fiy may be present simultaneously or successively on the test image 10.

[0052] To accomplish the first two steps of sloped calibration of thisembodiment variant, with camera 2 we observed the viewed points M′iimage of the points M″i after reflection at points Mi, and a singlecorrespondence is established between the intensity I′i of the viewedpoints M′i and the coordinate zi of the mirror 12, on the one hand, andthe coordinates xi, yi of points Mi, on the other hand. By a method suchas temporal phase shift, spatial phase shift, or direct calculation ofthe phase by means of the Fourrier transform of the image of intensitiesI′ix, I′iy if the intensities Iix, Iiy are modulated sinusoidally, or byany other method, the observed intensities I′ix, I′iy are connected withthe coordinates xi″ yi″. Therefore, we know the coordinates x″i, y″i ofthe reference point M″i of the test image 10, whose image is observed atthe viewed point M′i or pixel after reflection of the point Mi of thesurface to be measured S. The next part of the sloped calibration phasecan be accomplished as indicated above.

[0053] The sloped calibration phase is followed by the slope measuringphase of the optically reflective surface to be measured S illustratedby FIG. 5.

[0054] In a first step, we place in the measuring space 1 the opticallyreflective surface to be measured S, of which we know at least thecoordinate zr along axis Z of at least one point Mr. This point Mrcorresponds, for example, to a mechanical abutment or to any point onthe surface to be measured S whose coordinate zr is known and measuredseparately, for example, by means of a sensor. The camera 2 is used toobserve the viewed point M′r, image of the reference point M″r of thetest image 10 after reflection on the surface S at point Mr. By locatingthe point Mr, for example by a visual means, we observe the coordinatesx′r, y′r of the corresponding viewed point M′r. Knowing the coordinatezr along axis Z, using the preceding single correspondence, we candeduce from it the coordinates xr, yr of point Mr in the specialreference mark O, X, Y, Z.

[0055] In a second step, we determine the normal vector Nr at point Mr.According to the laws of the reflection and with reference to FIG. 4, weknow that if M″i is the reference point belonging to the test image 10,Mi is the corresponding point on the surface to be measured S, and M″cis the optical center of the lens of camera 2, mm″ is the unit vectorthat is colinear to MiM″i, mm′ is the unit vector that is colinear toMiM″c, Ni is the normal vector at the surface of point Mi, vectors mm″,mm′, and Ni are linked by the relation mm″+mm′=k×Ni, in which k is ascalar magnitude. Therefore, to define the normal vector Nr at point Mr,we apply this same relation which is then written mrmr″+mrmr′=k. Nr withMr″ reference point of the test image 10, whose image is the viewedpoint Mr′ formed after reflection on the surface to be measured S atpoint Mr, of which we know the coordinate zr along the axis Z, mrmr″ theunit vector colinear with MrM″r, mrmr′ the unit vector colinear withMrM″c. Transposed on the axes X, Y, Z, this relation yields a system ofequations making it possible to determine the normal vector Nr in Mr onthe surface to be measured S, and therefore the slopes Prx, Pry alongthe axes X and Y at this point.

[0056] In a third step, we consider a point Mr+1 near Mr, of which wedecide temporarily and arbitrarily that the theoretical coordinatezr+1th along axis Z is approximately equal to zr. We observe thecoordinates x′r+1, y′r+1 of the viewed point M′r+1 image of Mr+1 of thesurface to be measured S. Knowing x′r, y′r and the coordinate zr+1th bymeans of the previous calibration, we determine the coordinates xr+1,yr+1 of the point Mr+1. We measure the intensities I′ix and I′iy, ofwhich we determine the coordinates x″r+1 and y″r+1 of the referencepoint M″r+1 of the test image 10. Knowing the coordinates xr+1, yr+1,and zr+1th of Mr+1, the coordinates x″r+1 and y″r+1 of M″r+1, and thecoordinates of point C, by solving the system of equations describedabove, we determine the normal vector Nr+1 at point Mr+1 on the surfaceto be measured S.

[0057] Knowing Mr and Nr+1, knowing xr+1 and yr+1, and being aware thatNr+1 is orthogonal to MrMr+1, we determine the true coordinate zr+1 byposting that the scalar product MrMr+1 by Nr+1 is equal to zero, whichyields an equation in which the unknown is zr+1. The slopes Pr+1x, Pr+1yare calculated directly from Nr+1 by means of the following ratios:Pr+1x=Nr+1x/Nr+1z and Pr+1y=Nr+1y/Nr+1z in which Pr+1x and Pr+1y are,respectively, the slopes along the axes X and Y at point Mr+1, Nrx, Nryand Nrz are projections, respectively along axes X, Y, and Z of vectorNr.

[0058] We can then perform an iterative calculation to refine theresults and increase the precision of the coordinate zr+1.

[0059] By repeating this measuring phase from one point to the next, foreach point of the surface to be measured S, we define the whole of theslopes Pix, Piy along the axes X and Y, and the whole of the coordinatesxi, yi, zi of the points Mi viewed at points M′i by the camera 2. Theslopes Pix, Piy of any point intermediate to two measured points can beobtained by interpolation of the slopes of the nearby points measured.In this way, at any point Mi of the surface to be measured S, we candetermine the slopes Pix, Piy along axes X, Y respectively.

[0060] The measuring device according to the invention which permits theuse of the process for measuring at least one geometric magnitude of anoptically reflective surface to be measured S described above includes,in particular, at least one measuring space 1 in which we place at leastone reference surface P, Ci, or surface to be measured S, at least onetest image 6, 10 positioned to reflect on the reference surface P, Ci,or surface to be measured S, and at least one camera 2 position so thatits field of view 3 covers the measuring space 1 and sees the reflectionof the test image 6, 10 on the reference surface P, Ci or surface to bemeasured S. The camera 2 is associated with a computer system (notshown) designed to interpret the image of the optically reflectivesurface to be measured S viewed by the camera 2 and to deduce from itthe quantitative values characterizing at least one geometric magnitudeof the surface to be measured S as a function of at least one referencesurface P, Ci, with a photograph from camera 2 permitting visualizationof all the points of the surface to be measured S.

[0061] Possibilities for Industrial Application

[0062] This description clearly shows that the process according to thisinvention permits the calibrated measuring device to measure oncerapidly and accurately one or more geometric magnitudes of largeoptically reflective surfaces by determining, depending on the methodused, the curvature of a point on the surface to be measured or theslope at each point of the optically reflective surface to be measuredand the position in the measuring space of each of these points.

[0063] This invention is not limited to the embodiment examplesdescribed, but extends to any modification and variant that are apparentto a person skilled in the art, while remaining within the protectiondefined in the attached claims.

1. A process for measuring at least one geometric magnitude of anoptically reflective surface, comprising the steps of: creating acalibration system; viewing an image of the optically reflective surfaceby a camera associated with a computer; and transforming the image ofthe optically reflective surface viewed by said camera into quantitativevalues using the calibration system.
 2. The process according to claim1, wherein the calibration system is created by defining a measuringspace with which an orthonormed spatial reference mark O, X, Y, Z isassociated, and in said measuring space (1) there is at least onereference surface P, Ci or the optically reflective surface; said camerais disposed in such a way that its field of view covers said measuringspace and sees said reference surface P, Ci or the optically reflectivesurface; associated with said image there is a plane reference mark O′,X′, Y′; a test image (6,10) is associated with a plane reference markO″, X″, Y″ and comprises reference points M″i, so that said referencepoints M″i are reflected on said surface P, Ci and the opticallyreflective surface, in points Mi; with said camera, the viewed pointsM′i image of said reference points M″i after reflection on said surfaceP, Ci and the optically reflective surface at said points Mi can beobserved, and a single correspondence is established between said viewedpoints M′i and said reference points M″i.
 3. The process according toclaim 2 wherein the creation of the calibration system includes a stepof establishing a single correspondence between the coordinates x′, y′of said viewed points M′i and the coordinates x, y of said points Miwhose coordinate along axis Z is known.
 4. The process according toclaim 2 wherein said camera is disposed in such a way that its field ofview is oblique with respect to said reference surface Ci; said testimage is disposed in such a way that it is situated opposite said camerawith respect to said reference surface Ci, and said camera is focusedessentially on said reference surface Ci.
 5. The process according toclaim 3 wherein the reference surface includes at least one standardcurve Ci having at least one known curvature 1/Ri along axes X, Y, saidcamera is used to observe said viewed points M′i image of said referencepoints M″i of said test image after reflection on said standard curve Ciat points Mi, and a single correspondence is established between themeasured values or their variations at said viewed points M′i and saidcurvature 1/Ri of said standard curve Ci.
 6. The process according toclaim 5 wherein said test image comprises a coding for intensity Iiand/or for color that varies from one point of the surface to another,this variation being defined by a known function along at least one axisX″, Y″ of said test image; said camera is used to observe said viewedpoints M′i image of said reference points M″i of said test image afterreflection on said standard curve Ci at points Mi, and in that a singlecorrespondence is established between the variation in intensity I′imeasured and/or the variation in color measured or their variations atsaid viewed points M′i, and said curvature 1/Ri of said standardcurvature Ci.
 7. The process according to either of claim 5 or 6 whereinsaid standard curve Ci forming said reference surface is shifted indifferent positions of said measuring space (1), and in that theobservation of said image viewed by said camera (2) is repeated, andsaid single correspondence is established in a number of points Midetermined as a function of the desired precision for said singlecorrespondence.
 8. The process according to any of claims 3 whereinseveral standard curves Ci are used, each having a different curvature1/Ri.
 9. The process according to any of claims 1-6 wherein theoptically reflective surface is placed in said measuring space, saidcamera is used to observe said viewed points M′i image of said referencepoints M″i of said test image (6) after reflection on said surface to bemeasured S at said points Mi, and the curvature 1/Ri at said points Mias a function of the laws of single correspondence resulting from saidcalibration system can be deduced.
 10. The process according to claim 3wherein the creation of the calibration system includes a slopecalibration whereby said test image is essentially opposite saidmeasuring space and said camera so that its optical center is disposedessentially in the vicinity of said test image (10) and in that areference surface at least one reference plane P is essentially parallelto said test image (10) and has a known coordinate along axis Z.
 11. Theprocess according to claims 3 and 10 wherein the sloped calibration isconducted by using an essentially flat mirror (12) with coordinate zialong axis Z, and in that said camera is used to observe said viewedpoints M′i image of said reference points M″i of said test image (10)after reflection on said reference surface P at said points Mi, and inthat said single correspondence is established between the coordinatesx′, y′ of said viewed points M′i and the coordinates x, y of said pointsMi of which the coordinate along axis Z is known.
 12. The processaccording to claim 11 wherein the mirror (12) forming said referenceplane P is shifted parallel to itself in different coordinates zi ofsaid measuring space, and in that the observation of said image viewedwith said camera is repeated, and said single correspondence isestablished.
 13. The process according to claim 12 wherein the testimage (10) comprises a coding for intensities Iix, Iiy and/or colorsthat vary from one point of the surface to another, these variationsbeing defined by known functions along, respectively said axes X″ and Y″of said test image (10), in that said camera is used to observe saidviewed points M′i image of said reference points M″i after reflection onsaid mirror (12) at points Mi, and in that the single correspondencesare established between, on one hand, the measured intensities I′ix,I′iy and/or the measured colors or their variations at said viewedpoints M′i, said coordinate zi of said reference plan P and, on theother hand, the coordinates xi, yi of said point Mi.
 14. The processaccording to any of claims 10 and 12-13 wherein the optically reflectivesurface is placed in said measuring space (1), said camera is used toobserve said viewed points M′i image of said reference points M″i ofsaid test image (6) after reflection on said surface to be measured S atsaid points Mi, and from it we deduce the coordinates xi, yi, zi at saidpoints Mi as a function of said laws of single correspondence resultingfrom said calibration phase, and the slopes Pix, Piy, respectively,according to the axes X and Y at points Mi.
 15. A system for measuringat least one geometric magnitude of an optically reflective surfacecomprising: at least one measuring space in which at least one referencesurface P, Ci for calibrating the system or the optical reflectivesurface is placed; at least one test image (6, 10) positioned to reflecton said reference surface P, Ci, or the optically reflective surface;and at least one camera positioned such that its field of view coverssaid measuring space and sees the image of said test image (6, 10) onsaid reference surface P,Ci or the optically reflective surface; whereinsaid camera associated with a computer system is adapted to transformthe image of said optically reflective surface viewed by said camera andto quantitative values that characterize the at least one geometricmagnitude of said optically reflective surface.
 16. The processaccording to claim 1 wherein the calibration system is created bydefining a measuring space, in which at least one reference surface P,Ci or the optically reflective surface is placed.
 17. The processaccording to claim 16 wherein the measuring space is defined byorthonormed spatial reference marks O, X, Y and Z.
 18. The processaccording to claim 17 wherein said camera is disposed in such a way thatits field of view covers said measuring space and sees said referencesurface P, Ci or the optically reflective surface.
 19. The processaccording to claim 18 further includes an image viewed by the camerahaving a plane reference mark O′, X′, Y′ with points M′i and a testimage (6,10) associated with a plane reference mark O″, X″, Y″ withreference points M″i, wherein said reference points M″i are reflected onsaid reference surface (P, Ci) and the optically reflective surface inpoints Mi, and a single correspondence is established between saidviewed points M′i and said reference points M″i.